Dynamics of matter-wave and optical fields in superradiant scattering from Bose-Einstein condensates

We study superradiant scattering off Bose-Einstein condensates by solving the semiclassical Maxwell-Schrödinger equations describing the coupled dynamics of matter-wave and optical fields. Taking the spatial dependence of these fields along the condensate axis into account, we are able to reproduce and explain many of the characteristic features observed in the experiments of Inouye et al. [Science 285, 571 (1999)] and Schneble et al. [Science 300, 475 (2003)], such as the shape of the atomic side-mode distributions for forward and backward scattering, the spatial asymmetry between forward and backward side modes, and the depletion of the condensate center observed for forward scattering.

Figure 1

Strong-pulse regime. (a) Spatial distribution of the first-order forward (1, $\pm 1$) and backward $(-1,\pm 1)$ atomic side modes, after applying a laser pulse of duration $t_f=14\mu \mathrm{s}$ and strength $g=2\times {10}^6{\mathrm{s}}^{-1}$ to the condensate followed by a free propagation for a time $t_p=25\mathrm{ms}$. (b) Spatial distributions of the atomic side modes and the optical endfire modes $\left({\mathcal{E}}_{\pm }\right)$, at time $t_f$. For the sake of illustration the BEC population (0, 0) has been divided by 4.

Figure 2

Atomic side-mode distributions. Each square represents an integrated probability $p_{nm}=\int dz{\mid {\psi }_{nm}(z,t)\mid }^2$. (a) Strong-pulse regime: $t_f=10.6\mu \mathrm{s}$ and $g=2.6\times {10}^6{\mathrm{s}}^{-1}$. (b) Weak-pulse regime: $t_f=232\mu \mathrm{s}$ and $g=5.0\times {10}^5{\mathrm{s}}^{-1}$. (c) Weak-pulse regime: $t_f=291\mu \mathrm{s}$ and $g=6.5\times {10}^5{\mathrm{s}}^{-1}$. (d) Spatial distribution of the condensate along the axis $z$ corresponding to (c).